Definition:Vector Space Automorphism
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Definition
Let $V$ be a $K$-vector space.
Let $\phi: V \to V$ be a vector space isomorphism to itself.
Then $\phi$ is a vector space automorphism.
Linguistic Note
The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.
Thus automorphism means self structure.